Max

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Max
x = 27, y = 27, rule = B3/S23 18bo$17b3o$12b3o4b2o$11bo2b3o2bob2o$10bo3bobo2bobo$10bo4bobobobob2o$ 12bo4bobo3b2o$4o5bobo4bo3bob3o$o3b2obob3ob2o9b2o$o5b2o5bo$bo2b2obo2bo 2bob2o$7bobobobobobo5b4o$bo2b2obo2bo2bo2b2obob2o3bo$o5b2o3bobobo3b2o5b o$o3b2obob2o2bo2bo2bob2o2bo$4o5bobobobobobo$10b2obo2bo2bob2o2bo$13bo5b 2o5bo$b2o9b2ob3obob2o3bo$2b3obo3bo4bobo5b4o$2b2o3bobo4bo$2b2obobobobo 4bo$5bobo2bobo3bo$4b2obo2b3o2bo$6b2o4b3o$7b3o$8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
Pattern type Spacefiller
Number of cells 187
Bounding box 27 × 27
Discovered by Tim Coe
Year of discovery 1995

Max is a spacefiller that was found by Tim Coe[1] in October 1995 that fills the plane with zebra stripes. In terms of its 187 cells, it was formerly tied with spacefiller 2 as the smallest known spacefiller, and in terms of its 27 × 27 bounding box it was the outright smallest for many years.[2]

In February 2020, Alex Greason and Adam P. Goucher found 26 × 26 and 25 × 25 predecessors to Max that improved on the bounding box at the cost of increased population.[3][4] In April, Mateusz Naściszewski found a 25 × 25 predecessor with a population of only 215,[5] as well as a Max variant with a 27 × 27 bounding box but a population of only 183 cells.[6] In November 2021, Rocknlol found several new patterns with LogicLifeSearch which separately break the records for smallest population (151) and bounding box (23 × 23) of known Max predecessors.[7] In December 2022, iNoMed constructed a 127-cell 27 × 23 variant of Rocknlol's 151-cell pattern;[8] a few days later Rocknlol found a 134-cell 21 × 21 variation as well as a 110-cell 27 × 23 variation. Both of these records were reduced further still to a 107-cell predecessor and a 21 × 19 predecessor.[9]

x = 25, y = 25, rule = B3/S23 6bo5bo3b3o2bo$7bob4obo2b2o2b3o$8b2ob2o2bo3bob2o$9bo4b3obo3bo$6bo7bobob obobobo$bo2bo3bo3b3obo2b5o$o4b3o2bo2bo2bo$o2bobob4o2bobo3bo3b2o$3ob2o 7bo$3bo2b4obo3bo2bo4bo$6bobobo2bo2bo7bo$3bo2b5obobobo2bobo2bo$3ob2o6bo 6b2ob3o$o2bobo2bobobob5o2bo$o7bo2bo2bobobo$bo4bo2bo3bob4o2bo$11bo7b2ob 3o$2o3bo3bobo2b4obobo2bo$8bo2bo2bo2b3o4bo$b5o2bob3o3bo3bo2bo$obobobobo bo7bo$2bo3bob3o4bo$2b2obo3bo2b2ob2o$b3o2b2o2bob4obo$3bo2b3o3bo5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
A smaller but higher-population grandparent of the Max spacefiller, by Mateusz Naściszewski (click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 27, rule = B3/S23 18bo$17b3o$12b3o4b2o$11bo2b3o2bob2o$10bo3bobo2bobo$10bo4bobobobob2o$ 12bo4bobo3b2o$4obobobobo4bo3bob3o$o3bo4b3ob2o9b2o$o5b2o3bobo$bo2bo4b2o 3b2o$8b2obobobobobobob4o$bo2bo4b2o2bo2b2o4bo3bo$o5b2o3bobobo3b2o5bo$o 3bo4b2o2bo2b2o4bo2bo$4obobobobobobob2o$11b2o3b2o4bo2bo$13bobo3b2o5bo$b 2o9b2ob3o4bo3bo$2b3obo3bo4bobobobob4o$2b2o3bobo4bo$2b2obobobobo4bo$5bo bo2bobo3bo$4b2obo2b3o2bo$6b2o4b3o$7b3o$8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
183-cell Max variant, by Mateusz Naściszewski (click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 23, rule = B3/S23 17b2o$17bob2o$12b3o3b2obob2o$11bo2b3o2bobobo$4b2o4bo3b2o5b3o$4bo5bo5bo bobo2bo$b4o7bo5bo$bo7bobo9bo2bobo$3bo2b2ob3ob2o6bobobo$o4bo3bobobo$bob o3bobo2bo2b2o7bo$2bob2o2bo2bobobo2bo2b2obo$2bo7b2o2bo2bobo3bobo$13bobo bo3bo4bo$bobobo6b2ob3ob2o2bo$obo2bo9bobo7bo$8bo5bo7b4o$3bo2bobobo5bo5b o$3b3o5b2o3bo4b2o$3bobobo2b3o2bo$2b2obob2o3b3o$6b2obo$8b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
151-cell 27 × 23 predecessor, by Rocknlol (click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 23, rule = B3/S23 20b3o$19bo2bo$19bo2bo$13b3o3bo3bo$12bo2bo2bo3bo$5b2o4bo3bo2bo6bo$5bo5b o10bo3bo$2b4o7bo3bobo2b5o$2bo7bobo11bo$4bo2b2ob3ob2o$6bo3bobobo2bo2b2o bo$b2obo3bobo2bo2bobo3bob2o$3bob2o2bo2bobobo3bo$11b2ob3ob2o2bo$2bo11bo bo7bo$5o2bobo3bo7b4o$o3bo10bo5bo$bo6bo2bo3bo4b2o$4bo3bo2bo2bo$3bo3bo3b 3o$4bo2bo$4bo2bo$4b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
127-cell 27 × 23 spacefiller, by iNoMed (click above to open LifeViewer)
RLE: here Plaintext: here
x = 27, y = 23, rule = B3/S23 20b3o$14bo5bo2bo$20bo$12bob2o4bo$12b4o4bo$12b2o3bo2bo$2b2o7bo9bo$2bo6b o3bo9bo$4b2o3bo3bo3b2o5bo$2o4b2obo3bo10bo$4bo6bo3bobobob3o$2bob2o2bo2b o3bo2bo2b2obo$3b3obobobo3bo6bo$2bo10bo3bob2o4b2o$2bo5b2o3bo3bo3b2o$3bo 9bo3bo6bo$5bo9bo7b2o$6bo2bo3b2o$6bo4b4o$6bo4b2obo$6bo$3bo2bo5bo$4b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
110-cell 27 × 23 spacefiller, by Rocknlol (click above to open LifeViewer)
RLE: here Plaintext: here
x = 21, y = 21, rule = B3/S23 11b2o4b3o$2bo13bo2bo$9bobo7bo$b2o10bo3bo2bo$2ob2obo2b2o2bo4bo$3bo2bo2b o3bo2bo$o8b3o3b2o3bo$o4b2o3b2o3bo2bo$2obobobo3bo2bo4b2o$bo3bob3obobo2b 2o2bo$3o4bo5bo4b3o$o2b2o2bobob3obo3bo$2o4bo2bo3bobobob2o$2bo2bo3b2o3b 2o4bo$o3b2o3b3o8bo$4bo2bo3bo2bo2bo$2bo4bo2b2o2bob2ob2o$o2bo3bo10b2o$bo 7bobo$bo2bo13bo$b3o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
134-cell 21 × 21 spacefiller, by Rocknlol (click above to open LifeViewer)
RLE: here Plaintext: here
x = 25, y = 23, rule = B3/S23 19b3o$13bo5bo2bo$13bo5bo$11bo2bo4bo$11b4o4bo$3bo7b2o3bo2bo$o9bo9bo$b2o 5bo3bo10bo$4bo3bo3bo9bo$2obob2obo3bo3b2o4bo$4bo5bo3b2o4bo3bo$2bob2o2bo 3bo3bo2b2obo$o3bo4b2o3bo5bo$2bo4b2o3bo3bob2obob2o$2bo9bo3bo3bo$bo10bo 3bo5b2o$4bo9bo9bo$5bo2bo3b2o7bo$5bo4b4o$5bo4bo2bo$5bo5bo$2bo2bo5bo$3b 3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
107-cell 25 × 23 predecessor, by Rocknlol (click above to open LifeViewer)
RLE: here Plaintext: here
x = 21, y = 19, rule = B3/S23 8bo2b3o3b3o$bo5bo3b2o4bo2bo$ob3ob3o8bo$2bo2b2o3b3o3bobo$o4bo3b2obob2o 2bo$2obo2bo7b2ob3o$2bo4bo3b4obo2bo$11bobo$3b4o2bo2bobo2b2obo$4o4bo3bo 4b4o$ob2o2bobo2bo2b4o$7bobo$bo2bob4o3bo4bo$b3ob2o7bo2bob2o$2bo2b2obob 2o3bo4bo$2bobo3b3o3b2o2bo$3bo8b3ob3obo$o2bo4b2o3bo5bo$b3o3b3o2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 ]]
142-cell 21 × 19 predecessor, by Rocknlol (click above to open LifeViewer)
RLE: here Plaintext: here

Alternatively, the term Max may be used to describe whatever the smallest-known spacefiller is at the current time. The term represents the fact that the growth rate is the fastest possible of any pattern in Conway's Game of Life.[10]

Image gallery

Max at generation 50

See also

References

  1. Coe's improvements on the spacefiller at Paul Callahan's Page of Conway's Life Miscellany
  2. Spacefiller.lif in Alan Hensel's lifebc.zip pattern collection.
  3. Alex Greason (February 15, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  4. Adam P. Goucher (February 16, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  5. Mateusz Naściszewski (April 16, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  6. Mateusz Naściszewski (April 17, 2020). Message in #cgol on the Conwaylife Lounge Discord server
  7. Rocknlol (November 17, 2021). Small Spacefillers (discussion thread) at the ConwayLife.com forums
  8. iNoMed (December 29, 2022). Re: Small Spacefillers (discussion thread) at the ConwayLife.com forums
  9. Rocknlol (January 8, 2023). Re: Small Spacefillers (discussion thread) at the ConwayLife.com forums
  10. "Max". The Life Lexicon. Stephen Silver. Retrieved on May 24, 2009.

External links